Zulu (and any other proper OpenJDK build) has no functional or performance advantages or disadvantages when compared to the Oracle JDK of a matching version. The two are pretty much build from the same sources, licensed under (very) different terms. I would expect pretty much all measurements comparing the two to show "equal to within measurement noise". That's certainly what we've seen whenever a comparison was done.
<disclaimer: "I am not a lawyer">
The licensing advantages of Zulu (and other OpenJDK builds) is very real, and goes well beyond "I want to support and use open source": Zulu is not only free to use. It is freely redistributable. This means that you can safely include a full JDK in packages, guest OS images, docker images, AMIs, etc., and you don't have to worry about redistribution of those bits (e.g. by placing them in a public repository or letting someone else download them from a repo) crossing the commercial license terms and restrictions on redistribution that other JVMs may include with.
I can't speak for others and their licenses, but I'm pretty sure that hiding a script that downloads a free (but not freely redistributable) JDK and auto-answers "yes" to it's license questions without the third party end user actually knowing that a license is being accepted on their behalf is a no no. Sort of like signing someone else name on a check. For an example of something that is probably not a good idea to to be given to third parties, see this
dockerfile. Zulu doesn't have that restriction, and you can use docker file
like this one without worrying about redistribution restrictions and hidden license acceptance.
</ "I am not a lawyer" disclamer>
And if you are looking for better functionality and behavior metrics, a kick-ass JVM, and benefits like putting an end to GC tuning and code-arounds, or ReadyNow warmup benefits, thats where Zing (Azul's flagship product) comes in. Think of Zulu as a "vanilla OpenJDK", while Zing is a banana split with a cherry on top.